I want to divide the surface of a donut into as many different regions as possible. The regions can be any shape, as long as they are each in one piece. Each region must touch each of the other regions (touching on a corner doesn't count). How many regions can I make?

I am sorry that I have overlooked the question.  I did not realise the phrase, each region must touch each of the other regions (touching on a corner doesn't count), is mentioned in the question.  Ignore my answer previously.

The correct answer has been submitted by Hugo in his latest comment to be 8 sections and it is made up of 4 parts.  His answer is absolutely correct and non-debatable.

Edited on April 23, 2005, 5:46 pm

Posted by Jonathan Chang on 2005-04-23 17:06:02